Groupoid C*-Algebras with Hausdorff spectrum

Research output: Contribution to journalArticle

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Abstract

Suppose that G is a second countable, locally compact Hausdorff groupoid with abelian stabiliser subgroups and a Haar system. We provide necessary and sufficient conditions for the groupoid C* -algebra to have Hausdorff spectrum. In particular, we show that the spectrum of C*(G) is Hausdorff if and only if the stabilisers vary continuously with respect to the Fell topology, the orbit space {G}(0) G is Hausdorff, and, given convergent sequences χi → χ and γi ̇ χi →ω in the dual stabiliser groupoid S where the γi G act via conjugation, if χ and ω are elements of the same fibre then χ = ω.

Original languageEnglish (US)
Pages (from-to)232-242
Number of pages11
JournalBulletin of the Australian Mathematical Society
Volume88
Issue number2
DOIs
StatePublished - Oct 1 2013

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Groupoid
C*-algebra
Fell Topology
Haar System
Second countable
Orbit Space
Convergent Sequence
Locally Compact
Conjugation
Fiber
Vary
Subgroup
If and only if
Necessary Conditions
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Groupoid C*-Algebras with Hausdorff spectrum. / Goehle, Geoff.

In: Bulletin of the Australian Mathematical Society, Vol. 88, No. 2, 01.10.2013, p. 232-242.

Research output: Contribution to journalArticle

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